1.In “… non quidem cessatur adhuc, sed festinetur” (Seneca, Epistulae morales ad Lucilium, XXVII.4) the two verbs are in the passive voice because they are used in the impersonal form, as having no personal subject, and then are used in the third person singular, passive voice (See AG 207).
So, “… non quidem cessatur adhuc, sed festinetur” literally means:”… not yet indeed (non quidem …adhuc) it is ceased (cessatur, present indicative, passive, 3rd person singular, impersonal) , but let it is hurried (sed festinetur, 3rd sg pres subj pass, impersonal form)” i.e. “…thus far we have indeed not been idle, but let’s hurry” with reference to the fact that we must hurry to look for virtue and the joy which virtue produces.

2. “Nemo vetulus nomenclator, qui nomina non reddit sed imponit, tam perperam tribus quam ille Troianos et Achivos persalutabat” (XXVII.5) literally means:” No (nemo) old (vetulus) slave nomenclator (nomenclator) who (qui) does not prompt (reddit) the names (nomina), but (sed) invents (inponit) [them], saluted one after another (persalutabat) [his master's] tribesmen (tribus, 4th declension, direct object, accusative plural) so (tam) wrongly (perperam) as (quam) he (i.e. Calvisius Sabinus) [mistook] the Trojans (Troianos) for the Achaeans (et Achivos)”.
So, when Seneca says that no old slave nomenclator (i.e. the slave who had to tell his master the right names of those he met in the street) who invents the names, instead of saying them correctly, can make so many mistakes as a certain rich man named Calvisius Sabinus who mistakes the Trojans for the Achaeans for his memory is faulty, he wants to mean that such Calvisius Sabinus, who however desired to appear learned, made more mistakes than a slave nomenclator who invented the names of those whom his master met in the street.
In short, Seneca wants to point out how Calvisius Sabinus was forgetful and ignorant, though he believed that what any slave of his household knew, he himself knew also (See XXVII.7: “Ille tamen in ea opinione erat, ut putaret se scire, quod quisquam in domo sua sciret”). Nobody, in fact, no matter how rich he is, is able to borrow or buy wisdom (See XXVII. 8:” Bona mens nec commodatur nec emitur”).

3.Here’s the literal translation for “… non invenerat, faciendos locavit”(XXVII.6):”…he (i.e. Calvisius Sabinus) did not find (non invenerat ) [them, i.e. the slaves already educated], so he arranged/disposed (locavit) [them] to be learned (faciendos, gerundive used as an adjective of necessity depending on “locavit”)”.
In short, though Seneca’s style is quite concise, he wants to say that Calvisius Sabinus paid high prices for slaves since one had to know Homer by heart and another to know Hesiod, and another else each of the nine lyric poets, and when he did not find them ready to hand, i.e. already educated, he had them made to be educated: hence the high prices that he had to pay for such educated slaves.

4. In “Habebat ad pedes hos, a quibus subinde cum peteret versus, quos referret, saepe in medio verbo excidebat “(XXVII.6) the conjunction “cum”, which governs the imperfect subjunctive “peteret”, means “when” so that “Habebat ad pedes hos, a quibus subinde cum peteret versus….”literally means:”He had (habebat) at his feet (ad pedes) these slaves (hos) [from] whom (a quibus) when he asked (cum peteret) from time to time (subinde) verses (versus) which he had to repeat (quos referret), often (saepe) he broke down (excidebat) in the middle of a word (in medio verbo) “.
In short, Calvisius Sabinus used to have these educated slaves at his feet (i.e. at the foot of his dining table/ triclinium) so that he asked them from time to time for verses which he might repeat, but however he frequently broke down in the middle of a word simply because his memory was faulty.